Maximal Inequalities of Kahane-Khintchine’s Type in Orlicz Spaces
نویسنده
چکیده
Several maximal inequalities of Kahane-Khintchine’s type in certain Orlicz spaces are proved. The method relies upon Lévy’s inequality and the technique established in [14] which is obtained by Haagerup-Young-Stechkin’s best possible constants in the classical Khintchine inequalities. Moreover by using Donsker’s invariance principle it is shown that the numerical constant in the inequality deduced by the presented method is near to be as optimal as possible: If f "i j i 1 g is a Bernoulli sequence, and k k denotes the Orlicz norm induced by the function (x) = e 2 1 for x 2 R ; then the following inequality is satisfied:
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Best Constants in Kahane-Khintchine Inequalities in Orlicz Spaces
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